Maddon says Rafael Soriano to join Cubs on Monday
Following Sunday's 4-1 victory over Atlanta, Maddon said that Soriano will return to the majors after pitching a combined seven games at Double-A Tennessee and Triple-A Iowa.
Chicago signed the 35-year-old Soriano to a pro-rated contract on June 12.
Jackson went 16-34 with a 5.37 ERA in 82 games, including 58 starts, after signing a four-year, $52 million contract with the Cubs in January 2013.
Jason Motte is the Cubs' current closer.